If I understand your question correctly, then "I were thinking" for the past is incorrect. It'd only be correct if "it were" the subjunctive, for hypothetical situations: "If I were a native Italian, I would speak fluent Italian." Vs. "I was a native Italian, and so I spoke fluent Italian."
I was surprised that my translation " I was thinking of the same thing" was not accepted as correct. I grew up using , hearing other English speakers say " to think of (something), to think about something or somebody. Spanish speakers would always say" pensar en (algo) pensar en alguien . What I remember is that one should not translate word for word. Instead, translate the foreign sentence in the manner that is acceptable in your language.
I think the problem is your including "of". "I was thinking the same thing" and "I was thinking OF the same thing" aren't expressing the same idea. The former means that "you" and someone else were thinking alike, you both had the same idea about something. The latter is more specific and means that "you" and the other person were both thinking OF the same object, which might imply you agree about it, but that's not necessarily the same as thinking alike. E.g You & someone else find out that you both want to buy a car, because you both need one. So you're thinking of the same thing, namely a new car. That doesn't mean you both feel it's the right time or the right price to actually buy the car. You're thinking OF the same thing, a new car, but you aren't necessarily thinking the same way, alike. Including OF doesn't sound like much of a difference, but I believe there is.
urboydoms: 'would think' comes across more as a hypothetical, requring the subjunctive in English: "I would think the same thing...if I were the student." for example. "Would" can certainly be used for an habitual action in the past, as in "When I was a kid, I would always think about going to the zoo." But without a clearer context, your suggestion sounds more like the subjunctive use of 'would' than the English past, which is what the italian form 'pensavo' is.
"I thought the same thing" was about the fifth arbitrary rejection in this particular exercise. The worst was "Were you thinking of me?" which for some reason one was supposed to know "you" was plural, which is a very odd assumption. I don't like when someone answers "it depends on the context" because we are given no context. That's why these arbitrary "answers" are so annoying.
"I thought..." should have been accepted & should be reported. As regards "you" plural, I'd have to see the original -- if the exercise was a translation into Italian DL usually accepts tu, voi, or Lei -- assuming the dreaded context isn't clearer. If it's a translation into English, then use of those pronouns or in their absence the verb form should clearly tell you which one to use. That's not arbitrary at all.
Sagitta145, Captainlag27, and porcupine:
Germanlehrerlsu has already provided a convincing argument above as to the slight difference. In addition, the Italian phrase doesn't contain a word for "of". Your ability to learn a new language will be greatly enhanced if you can set aside your own preferences for the phrasing that you normally use and focus specifically on the grammar and vocabulary presented in the lesson.